GEOMETRY
What is the perimeter of a square that has an area of 25?
20
If x-2 = 64, what is the value of x1/3 + x0?
3/2
If 1/3 of a number is 4 less than 1/2 of the number, the number is
24.
Let x represent the unknown number. Since 1/3 of x is 4 less than 1/2 of x, x/3 = x/2 - 4. So, 2x = 3x - 24, giving x = 24.
If (23)2 = 4p, then 3p =
27
In how many different ways can five students be seated in three chairs?
60 ways
5x4x3=60
What is the area of a circle in which a 3 by 4 rectangle is inscribed?
25pi
Let the function f be defined by f(x) = 3x-1 and let the function g be defined by g(x) = x2. If m is a positive number such that f(7) = g(m) + g(2), what is a possible value of m?
4
Susan weighs p pounds. If Susan gains 17 pounds, she will weigh as much as Carol, who weighs 8 pounds less than Judy. If Judy weighs x pounds, then Susan's weight, p, in terms of x is
x-25
The sum of three consecutive integers is 72. What is the smallest of these three integers?
The smallest is 23.
The integers are 23, 24, 25
The cost of admission to an event is $5.00 plus one half of its price. How much does the event cost?
$10.00
Because $5 + 0.5($10) = $10.
At a certain time of day, a 25-foot telephone pole casts a 10-foot shadow. At that same time, how high would a tree have to be in order to cast a 25-food shadow?
62.5 feet.
Proportional reasoning with similar triangles.
A culture of 5000 bacteria triples every 15 minutes. What is the size of the bacteria population after 2 hours have elapsed? (Calculator needed.)
32,805,000
A boat moored in Richardson Bay (Sausalito) has a ladder that hangs down from the deck of the boat and touches the flat sea surface. The rungs are 1 foot apart. At low tide, ten rungs of the ladder are exposed. At high tide, the water level rises 6 feet. How many of the rungs will remain exposed?
5 rungs. This number of rungs will be exposed. As the tide comes in, the boat will rise up.
Simplify completely (x + 2)2 - x2
4(x+1)
Note: x2 + 4x + 4 - x2
Three fair coins are tossed at the same time. What is the probability that all three coins will come up heads OR all will come up tails?
1/4.
1/8 (all heads) + 1/8 (all tails) = 1/4.
If the integer lengths of the three sides of a triangle are 4, x, and 9, what is the least possible perimeter of the triangle?
19.
4 + x >9, x + 9 >4, 9+ 4 >x
Possible values of x are: 5 < x < 13
Least possible perimeter: 4 + 5 + 9 = 19
What is the equation of the graph obtained by shifting the graph of y=x2 horizontally to the left 4 units and vertically down 3 units?
y = (x+4)2 - 3
A father is currently 3 times as old as his son. In 12 years, the father will be twice as old as his son. How old is the father now?
x = age of father today, y = age of son today
System of equations:
x = 3y, x +12 = 2(y +1 12)
The son is currently 12, father is 36.
In 12 years: son will be 24, father will be 48, which is exactly twice 24
For the system of three equations:
x-z=7 x+y=3 z-y=6
what is x?
8
A 20-foot ladder leans against a wall. If the base of the ladder is 12 feet from the wall, how high up the wall does the ladder reach?
16 feet.
What is the number of sides of a polygon in which the sum of the degree measures of the interior angles is 4 times the sum of the degree measures of the exterior angles?
10.
Sum of the degree measures of exterior angles is 360.
S = (n-2)180 = 4 x 360, where n=number of sides. Solving for (n-2) = 8 or n=10.
If f(x) = 2x - 3 and g(x) = x3 + 1, find the value of x when f(g(x)) = 15.
x = 2
Fruit for a dessert costs $1.20 a pound. If 5 pounds of fruit are needed to make a dessert that serves 18 people, what is the cost of the fruit needed to make enough of the same dessert to serve 24 people?
$8.00.
If 5 pounds of fruit serve 18 people, then 5/18 pound serves one person, so 24 x 5/18 = 20/3 pounds. Since the fruit costs $1.20 a pound, the cost of the fruit needed to serve 24 people is 20/3 x $1.20 = $8.00.
For how many integer values of b is b+3>0 and 1>2b-9?
Seven.
b>-3, and b<5. Since b is an integer, b may be equal to any of the following: -2, -1, 0, 1, 2, 3, or 4.
x, y, 22, 14, 10... In this sequence, each term after the first term x is obtained by halving the term that comes before it and then adding 3 to that number. What is the value of x-y?
32
x=70, y=38. 70-38=32.